This is a recurrent question, nevertheless not frequent, but worth mentioning. Short answer is: No. A longer approach requests a bit more text:
1) As author of an original work you have all the rights upon that work whether you register it on official or private institutions or not. Registrations are declarative: Thet do not give any rights as you already have them all (still there are some remarks you should consider).
3) That you have now all the rights of a work doesn’t mean you will always keep them because, yes as you guessed, if you voluntarily give some of them away, you no longer have them all. No matter you registered or not. Both are separated issues.